A linear bounded operator T on an infinite dimensional separable complex Hilbert space H is said to satisfy property (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$UW_E$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>U</mi> <msub> <mi>W</mi> <mi>E</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>) if the complement in the approximate point spectrum of the essential approximate point spectrum coincides with the isolated eigenvalues of the spectrum. Via the CI spectrum induced by consistent invertibility property of operators, we explore property (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$UW_E$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>U</mi> <msub> <mi>W</mi> <mi>E</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>) for T and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$T^$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>T</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation> simultaneously. Furthermore, the transfer of property (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">$UW_E$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>U</mi> <msub> <mi>W</mi> <mi>E</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>) from T to f(T) and <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$f(T^{})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mmultiscripts> <mi>T</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is obtained, where f is a function which is analytic in a neighborhood of the spectrum of T. At last, with the help of the so-called (A, B) entanglement stable spectra, the entanglement stability of property (<InlineEquation ID="IEq8"> <EquationSource Format="TEX">$UW_E$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>U</mi> <msub> <mi>W</mi> <mi>E</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>) for <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$2\times 2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mo>×</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> upper triangular operator matrices is investigated.

Entanglement stability of property ($UW_E$)

期刊论文
发表日期：

2025年10月21日

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Sinan Qiu,
Lining Jiang

摘要

A linear bounded operator T on an infinite dimensional separable complex Hilbert space H is said to satisfy property ( $UW_E$ $U W_{E}$ ) if the complement in the approximate point spectrum of the essential approximate point spectrum coincides with the isolated eigenvalues of the spectrum. Via the CI spectrum induced by consistent invertibility property of operators, we explore property ( $UW_E$ $U W_{E}$ ) for T and $T^*$ $T^{*}$ simultaneously. Furthermore, the transfer of property ( $UW_E$ $U W_{E}$ ) from T to f(T) and $f(T^{*})$ $f (T^{*})$ is obtained, where f is a function which is analytic in a neighborhood of the spectrum of T. At last, with the help of the so-called (A, B) entanglement stable spectra, the entanglement stability of property ( $UW_E$ $U W_{E}$ ) for $2\times 2$ $2 \times 2$ upper triangular operator matrices is investigated.

Entanglement stability of property (\(UW_E\))

摘要